aa section 1-2
DESCRIPTION
What Is a Function?TRANSCRIPT
SECTION 1-2What Is a Function?
Warm-upTo determine the retail price a of the androids that Matt
Mitarnowski sells, he multiplies the wholesale price p by 1.75. Write an equation showing the situation and make a table
showing 6 values.
Warm-upTo determine the retail price a of the androids that Matt
Mitarnowski sells, he multiplies the wholesale price p by 1.75. Write an equation showing the situation and make a table
showing 6 values.
a = 1.75p
Warm-upTo determine the retail price a of the androids that Matt
Mitarnowski sells, he multiplies the wholesale price p by 1.75. Write an equation showing the situation and make a table
showing 6 values.
a = 1.75p
p $1.00 $2.00 $3.25 $17.32 $8.00 $9.14
a $1.75 $3.50 $5.69 $30.31 $14.00 $16.00
Dependent Variable:
Dependent Variable: The value that depends on another variable
Dependent Variable: The value that depends on another variable
Independent Variable:
Dependent Variable: The value that depends on another variable
Independent Variable: The variable that determines the dependent variable; relies on nothing
Dependent Variable: The value that depends on another variable
Independent Variable: The variable that determines the dependent variable; relies on nothing
Question:
Dependent Variable: The value that depends on another variable
Independent Variable: The variable that determines the dependent variable; relies on nothing
Question: Why do we call them dependent and independent variables?
Function:
Function: A pairing between two variables so that the independent variable matches with only one dependent variable.
Function: A pairing between two variables so that the independent variable matches with only one dependent variable.
“Is a function of ”:
Function: A pairing between two variables so that the independent variable matches with only one dependent variable.
“Is a function of ”: Statement used when we have a function
Function: A pairing between two variables so that the independent variable matches with only one dependent variable.
“Is a function of ”: Statement used when we have a function
[Dependent variable] is a function of [independent variable]
Example 1The table below shows the average temperature T in Fahrenheit
for each month M in Annville, PA.
M Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
T 35 39 49 61 71 79 83 81 73 63 51 40Source: http://www.weather.com/outlook/travel/vacationplanner/vacationclimatology/monthly/USPA0042
a. Is T a function of M? b. Is M a function of T?
Example 1The table below shows the average temperature T in Fahrenheit
for each month M in Annville, PA.
M Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
T 35 39 49 61 71 79 83 81 73 63 51 40Source: http://www.weather.com/outlook/travel/vacationplanner/vacationclimatology/monthly/USPA0042
a. Is T a function of M? b. Is M a function of T?
Yes, each month has only one average temperature
Example 1The table below shows the average temperature T in Fahrenheit
for each month M in Annville, PA.
M Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
T 35 39 49 61 71 79 83 81 73 63 51 40Source: http://www.weather.com/outlook/travel/vacationplanner/vacationclimatology/monthly/USPA0042
a. Is T a function of M? b. Is M a function of T?
Yes, each month has only one average temperature
Yes, each temperature is listed for only one month
Domain:
Domain: Anything that can possibly be substituted in for the independent variable
Domain: Anything that can possibly be substituted in for the independent variable
D = { }
Domain: Anything that can possibly be substituted in for the independent variable
Range:
D = { }
Domain: Anything that can possibly be substituted in for the independent variable
Range: Any value that can be listed as the dependent variable
D = { }
Domain: Anything that can possibly be substituted in for the independent variable
Range: Any value that can be listed as the dependent variable
D = { }
R = { }
Domain: Anything that can possibly be substituted in for the independent variable
Range: Any value that can be listed as the dependent variable
D = { }
R = { }
Input:
Domain: Anything that can possibly be substituted in for the independent variable
Range: Any value that can be listed as the dependent variable
D = { }
R = { }
Input: Another word for the independent variable
Domain: Anything that can possibly be substituted in for the independent variable
Range: Any value that can be listed as the dependent variable
D = { }
R = { }
Input: Another word for the independent variable
Output:
Domain: Anything that can possibly be substituted in for the independent variable
Range: Any value that can be listed as the dependent variable
D = { }
R = { }
Input: Another word for the independent variable
Output: Another word for the dependent variable
Example 2Give the domain and range of example 1.
M Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
T 35 39 49 61 71 79 83 81 73 63 51 40
Example 2Give the domain and range of example 1.
M Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
T 35 39 49 61 71 79 83 81 73 63 51 40
D = {Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec}
Example 2Give the domain and range of example 1.
M Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
T 35 39 49 61 71 79 83 81 73 63 51 40
D = {Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec}
R = {35, 39, 40, 49, 51, 61, 63, 71, 73, 79, 81, 83}
And now for some sets
And now for some sets
Natural Numbers:
And now for some sets
Natural Numbers: ℕ = {1, 2, 3, ...}
And now for some sets
Natural Numbers:
Whole Numbers:
ℕ = {1, 2, 3, ...}
And now for some sets
Natural Numbers:
Whole Numbers:
ℕ = {1, 2, 3, ...}
{0, 1, 2, 3, ...}
And now for some sets
Natural Numbers:
Whole Numbers:
Integers:
ℕ = {1, 2, 3, ...}
{0, 1, 2, 3, ...}
And now for some sets
Natural Numbers:
Whole Numbers:
Integers:
ℕ = {1, 2, 3, ...}
{0, 1, 2, 3, ...}
ℤ = {..., -3, -2, -1, 0, 1, 2, 3, ...}
And now for some sets
Natural Numbers:
Whole Numbers:
Integers:
Rational Numbers:
ℕ = {1, 2, 3, ...}
{0, 1, 2, 3, ...}
ℤ = {..., -3, -2, -1, 0, 1, 2, 3, ...}
And now for some sets
Natural Numbers:
Whole Numbers:
Integers:
Rational Numbers:
ℕ = {1, 2, 3, ...}
{0, 1, 2, 3, ...}
ℤ = {..., -3, -2, -1, 0, 1, 2, 3, ...}
ℚ; the set of numbers that can be written as a ratio
And now for some sets
Natural Numbers:
Whole Numbers:
Integers:
Rational Numbers:
Real Numbers:
ℕ = {1, 2, 3, ...}
{0, 1, 2, 3, ...}
ℤ = {..., -3, -2, -1, 0, 1, 2, 3, ...}
ℚ; the set of numbers that can be written as a ratio
And now for some sets
Natural Numbers:
Whole Numbers:
Integers:
Rational Numbers:
Real Numbers:
ℕ = {1, 2, 3, ...}
{0, 1, 2, 3, ...}
ℤ = {..., -3, -2, -1, 0, 1, 2, 3, ...}
ℚ; the set of numbers that can be written as a ratio
ℝ; any number that can be written as a decimal
Homework
Homework
p. 15 #1-23